Cohen-Macaulay and (S<sub>2</sub>) Properties of the Second Power of Squarefree Monomial Ideals

Cohen-Macaulay and (S<sub>2</sub>) Properties of the Second Power of Squarefree Monomial Ideals

We show that Cohen-Macaulay and (S<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>) properties are equivalent for the second power of a...

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Bibliographic Details
Main Authors: Do Trong Hoang, Giancarlo Rinaldo, Naoki Terai
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Mathematics
Subjects:
Stanley-Reisner ideal
edge ideal
Cohen-Macaulay
(S2) condition
Online Access:https://www.mdpi.com/2227-7390/7/8/684
Description
Summary:We show that Cohen-Macaulay and (S<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal <i>I</i> such that <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mo>/</mo> <msup> <mi>I</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> satisfies the Serre condition (S<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>), but is not Cohen-Macaulay.
ISSN:2227-7390

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